What is the value of the expression (1+x) (1+x2 ) (1+x4 ) (1+x8 )(1-x) ?

ABC26GN1259 · Simplification

Subject: General Aptitude · Chapter: Simplification · Exam: · Marks: · Difficulty:

What is the value of the expression $(1+x)\left(1+x^{2}\right)$ $\left(1+x^{4}\right)\left(1+x^{8}\right)(1-x)$ ?

(a)$x^{8}+1$

(b)$x^{16}-1$

(c)$1+x^{16}$

(d)$1-x^{16}$

Answer

Answer (as printed): D

Explanation

$(1+x)(1-x)(1+x^2)(1+x^4)(1+x^8) = (1-x^2)(1+x^2)(1+x^4)(1+x^8) = (1-x^4)(1+x^4)(1+x^8) = (1-x^8)(1+x^8) = 1-x^{16}$.

Explanation as extracted from the printed page; notation may be imperfect.